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Timetable (SIPW02)

Ice-fluid interaction

Monday 2nd October 2017 to Friday 6th October 2017

Monday 2nd October 2017
09:00 to 09:35 Registration
09:35 to 09:45 Welcome from David Abrahams (INI Director)
09:45 to 10:30 Hung Tao Shen (Other)
River Ice – Process, Theory, and Mathematical Modeling
River ice research has largely been driven by engineering and environmental problems that concern society. These concerns have been on ice jam flooding, hydropower operation, inland navigation, winter time ecology, and the influence of ice on water quality. River ice phenomena include formation, evolution, transport, accumulation, deterioration, and dissipation of various forms of ice. These phenomena involve complex interactions between hydrodynamic, mechanical, and thermal processes, under the influence of meteorological and hydrological conditions as well as the operations of water resources engineering projects. Most of the river ice phenomena also occur in sea ice, except that river ice forms in freshwater confined within channels. Mathematical modeling of river ice processes faces similar problems as sea ice, but in much smaller spatial and time scales because of the strong boundary effects. There has been only a relatively small group of researchers engaged in this no n-traditional topic of river hydraulics. However, important advances have been made in the last couple of decades. In this presentation, river ice processes and major research advances enabled by mathematical modeling will be discussed. These will include frazil and anchor formation, surface ice transport and ice jam dynamics, undercover frazil jam/hanging dam evolution, breakup processes, and sediment transport with ice effects.

Keywords: River ice, freeze up, frazil ice, ice jams, breakup, hydrodynamics, mathematical modeling 
INI 1
10:30 to 11:00 Morning Coffee
11:00 to 11:45 Mike Meylan (University of Newcastle, Australia)
Mathematical Challenges in Modelling Wave Scattering in the Marginal Ice Zone
When I started modelling wave scattering by sea ice in 1991, even the simplest two-dimensional model of wave scattering by a single ice floe had not been solved accurately. By 1996 I had developed three-dimensional models for an ice floe and a paradigm for the inclusion of scattering in wave prediction code. Some of this work was done during a month I spent at the Scott Polar Research Institute in Cambridge in 1995.Looking back, and returning to Cambridge 22 years later, it is striking (and slightly depressing) how progress on this topic has stalled. The reasons for this are largely mathematical and in this talk I will try and give a flavour of these difficulties and suggest some possible methods to tackle them.
INI 1
11:45 to 12:30 Stefanie Rynders (University of Southampton)
Modelling dynamics of the marginal ice zone, including combined collisional and EVP rheology
Co-authors: Yevgeny Aksenov (National Oceanography Centre), Daniel Feltham (Centre for Polar Observations and Modeling, University of Reading), George Nurser (National Oceanography Centre)

Exposure of large, previously ice-covered areas of the Arctic Ocean to the wind and surface ocean waves results in the Arctic pack ice cover becoming more fragmented and mobile, with large regions of ice cover evolving into the Marginal Ice Zone (MIZ). The need for better climate predictions, along with growing economic activity in the Polar Oceans, necessitates climate and forecasting models that can simulate fragmented sea ice with greater fidelity. The main focus here is on sea ice rheology. A Combined Collisional, reflecting the granular behaviour of MIZ sea ice, and Elastic-Viscous-Plastic (EVP) rheology is implemented in an idealised and a global sea ice-ocean model. The effect of surface waves on ice motion is included in the turbulent kinetic energy or ‘granular temperature’ of ice floes. The granular temperature is validated with accelerometer data. It is found that the combined rheology has impact beyond the marginal ice zone, influencing ice motion and sea ice thickness. Taking into account the fragmented nature of MIZ ice also allows for another dynamical feature of the MIZ: in idealised channel model simulations ice edge jets occur when variable floe size is used. The research leading to these results has received funding from the European Union's Seventh Framework Programme (FP7/2007-2013) under grant agreement n° 607476.
INI 1
12:30 to 13:30 Lunch @ Wolfson Court
13:30 to 14:15 Vernon Squire (University of Otago)
A different perspective on wave-ice interaction research
The focus of this talk will be on the two research strands that currently exemplify wave-ice interaction research, namely: (i) the continuum paradigm, which leads naturally into parametrizations that can potentially be incorporated straightforwardly into wave forecasting models such as WAVEWATCH III or global climate models; and (ii) methodology that endeavours to represent the physics of each constituent process as faithfully as possible, acknowledging from the outset that approximations are inevitable. The advantages and disadvantages of each approach will be discussed, especially in the context of implications for the design of field experiments and the subsequent analysis of any data collected. It is asserted that field experiments grounded in the continuum paradigm are particularly challenging because the number of degrees of freedom in Nature is huge compared with a typical model. The consequences of using a linear ansatz will also be made clear, recognizing that very nearly all current mathematical models of the phenomenon are linear yet the few data that are available suggest that the assumption of linearity is inconsistent with observation in some cases and presupposes outcomes that are too restrictive.
INI 1
14:15 to 15:00 John Grue (University of Oslo)
Dead water effect on drift of icebergs
Observations/measurements of the drift of an iceberg in Antarctica are motivation of the lecture. Particularly two measurements of the internal waves generated by the iceberg are discussed. These measurements are connected to Fridtjof Nansen's historical observations of the dead water on FRAM, published in Nansen (1897). The dead water resistance on FRAM is first obtained empirically from Nansen's observations. A strongly nonlinear interfacial model of the dead water resistance is then outlined with calculations relevant to the FRAM ship. The intersection of the resistance curves obtained empirically and theoretically determines accurately the speed of FRAM. This intersection becomes a function of the level of the pycnocline. The nonlinear and linear dead water wakes are then obtained at the low subcritical speeds. The connection between the dead water effect on FRAM and the ice berg case are discussed. The considerable increase in the dead water resistance at small subcritical speed, which FRAM did not overcome, is discussed. The same resistance slope seems to limit the speed of the iceberg drift where the observed internal wave Froude number is subcritical at a value of 0.6. References: J. Grue (2015). Nonlinear dead water resistance at subcritical speed. Phys. Fluids 27, 08213. J. Grue (2017). Calculating FRAM's dead water. In: The Ocean in Motion - Circulation, waves polar oceanography. Springer-Verlag, Oceanography Series. Eds. M.G. Velarde, R. Yu. Tarakanov, A.V. Marchenko. 70th Anniversary of Eugene G. Morozov. J. Morison and D. Goldberg (2012). A brief study of the force balance between a small iceberg, the ocean, sea ice, and atmosphere in the Weddell Sea. Cold regions science and technology, 76-77, 69-76.
INI 1
15:00 to 15:30 Afternoon Tea
15:30 to 16:15 Elizabeth Hunke (Los Alamos National Laboratory)
Where ice is not: The liquid phase in the sea ice model CICE
Viewed at a macroscopic scale, the liquid phase of the sea ice pack exhibits a stable, vertical density profile with relatively fresh melt water lying above saltier, denser brine within the ice and much denser seawater below. These layers interact through freezing, melting, dissolution and drainage processes. This talk will overview the representation of these processes in the sea ice model CICE, with indications of which ones may be important for simulating sea ice volume.
INI 1
16:15 to 17:00 Aleksey Marchenko (University Centre in Svalbard (UNIS))
Damping of surface wave in MIZ of the Barents Sea: field observations and modeling
Presentation will include an overview of field measurements of waves performed from drift ice in the Barents Sea since 2006. It includes observations of ice motion during events of wave propagation, measurements of sea current velocities in under ice boundary layer, water pressure at different depths, accelerations and angular velocities of floes. The data are used for the calculation of dispersion properties of observed waves and characteristics of under ice turbulence. The coefficient of wave attenuation is calculated using equation of floe motion along the water surface with relatively common assumptions about floe-floe interactions and known solution describing oscillating boundary layer near the bottom of floating ice. Numerical values of the coefficient are reconstructed using the data of field measurements. The evolution of wave spectra in MIZ of the North-West Barents Sea is compared with the wave spectra calculated from the high resolution satellite image (SAR).
INI 1
17:00 to 18:00 Welcome Wine Reception at INI
Tuesday 3rd October 2017
09:00 to 09:45 Luke Bennetts (University of Adelaide)
Modelling water wave overwash of ice floes
I will summarise progress towards modelling wave overwash of ice floes, which (after breakup) is arguably the most important nonlinear phenomenon in wave–ice interactions, and certainly the most striking one. The phenomenon is unique to wave–ice interactions, occurring because the small freeboards of ice floes allow waves with relatively modest (non-extreme) amplitudes to wash over their upper surfaces when differential motion between the floe and the surrounding wave field exists. Overwash impacts floes thermodynamically, and dissipates wave energy, thus reducing the distances waves penetrate into the ice-covered ocean. From a mathematical modelling perspective, it is a highly nonlinear phenomenon, meaning it cannot be captured by standard perturbation techniques. I will present a bespoke overwash model, along with supporting laboratory experiments and numerical CFD simulations. Applying the methodology to simplified versions of the problem will be shown to provide insights into model performance. 

Co-authors: David Skene (Uni Adelaide); Michael Meylan (Uni Newcastle); Alessandro Toffoli (Uni Melbourne); Filippo Nelli (Swinburne Uni Tech); Kevin Maki (Uni Michigan)
INI 1
09:45 to 10:30 Emilian I Parau (University of East Anglia)
Nonlinear hydroelastic waves and related flows
A review of some the results concerning nonlinear hdyroelastic waves will be given. We will present waves forced by moving pressures and solitary waves on top of a fluid covered by an ice plate, modelled as a thin elastic plate. The fluid is either of constant density of stratified and two-dimensional or three-dimensional problems are considered.
INI 1
10:30 to 11:00 Morning Coffee
11:00 to 11:45 Olga Trichtchenko (University College London)
Computing Flexural-Gravity Waves
Co-authors: Emilian Parau (University of East Anglia), Jean-Marc Vanden-Broeck (University College London), Paul Milewski (University of Bath)

In this talk we will discuss waves travelling under a layer of ice, which is represented as a thin elastic plate. We will compare and contrast different models for these types of waves and discuss the techniques involved in computing their solutions.
INI 1
11:45 to 12:30 Philippe Guyenne (University of Delaware)
Numerical study of solitary wave attenuation in a fragmented ice sheet
Co-author: Emilian Parau (University of East Anglia)

A numerical model for phase-resolved simulation of nonlinear ocean waves propagating through fragmented sea ice is proposed. This model solves the full time-dependent equations for nonlinear potential flow coupled with a nonlinear thin-plate formulation for the ice cover. The coefficient of flexural rigidity is allowed to vary spatially so that distributions of ice floes can be directly specified in the physical domain. Two-dimensional simulations are performed to examine the attenuation of solitary waves by scattering through an irregular array of ice floes.
INI 1
12:30 to 13:30 Lunch @ Wolfson Court
13:30 to 14:15 Pat Langhorne (University of Otago)
In situ detection of fluid movement in Antarctic land-fast sea ice
Co-authors: Pat Wongpan (University of Otago), Ken Hughes (University of Otago & University of Victoria), Inga J, Smith (University of Otago)

Vertical temperature strings are used in sea ice research to study heat flow, ice growth 
rate, and ocean-ice-atmosphere interaction. We demonstrate the feasibility of using temperature fluctuations as a proxy for fluid movement, a key process to resupply nutrients to 
Antarctic land-fast sea ice algal communities. Four thermistor arrays (including two mid-winter records) were deployed in the land-fast sea ice of McMurdo Sound, Antarctica. By 
smoothing temperature data with the robust LOESS method, we obtain temperature fluctuations that cannot be explained by insolation or heat loss to the atmosphere. Statistical 
distributions of these temperature fluctuations are investigated with sensitivities to the distance from the ice-ocean interface, average ice temperature, and sea ice structure. Temperature fluctu
ations are discrete events that have greatest magnitude close to the ice-ocean interface (< 50 mm) at temperatures > −3 &# x25E6;C. At temperatures > −3 ◦C fluctuations occur for 43% of the time, when the ice is colder (−3 to −5 ◦C) this active period is reduced to 11%. Assuming temperature fluctuations occur at a critical Rayleigh number derived from mushy layer theory, we parameterise a measure of permeability of this thick (>1 m) 
Antarctic land-fast sea ice in terms of average ice temperature. 
This permeability decreases by three orders of magnitude between the ice-ocean interface 
and ∼70 mm above it, as the sea ice temperature changes from the freezing point to −5 ◦C. 
 The same permeability parameterisation is independent of whether the sea ice has a columnar crystal structure or has a more disordered platelet ice structure, characteristic of proximity to an ice shelf. 
INI 1
14:15 to 15:00 Hayley Shen (Clarkson University)
Wave Propagation in Viscoelastic Materials over Water
Ice covers over water modify the mass, energy, and momentum transfer between the atmosphere and ocean. Ocean wave propagation is one of the numerous topics from these three basic processes. Because of the Arctic ice reduction, longer fetch has increased both the intensity and the dominant wave period. Longer period waves damp much less. They thus propagate further into ice covers. The contemporary Arctic system cannot be properly evaluated without a good grasp of the growing presence of waves under ice covers. Ice covers are complex materials. Even a continuous solid ice cover does not fit into a simple constitutive model. In the field ice covers often are consisted of discontinuous pieces of various sizes and shapes, mixed with open water or slurry of ice crystals. Such a composite cover has been idealized as a linear viscoelastic material. This hypothesis is based on a simple physical argument: all materials under deformation simultaneously store some and dissipate some energy. The first order approximation is therefore a linear viscoelastic model. To test this hypothesis, the dominant characteristics of the model must be thoroughly understood. The most important characteristic of wave propagation is the dispersion relation. Even with a simple linear viscoelastic model, the dispersion relation is complicated. There are many roots all satisfy the dispersion relation. All of them may be present under different conditions. In this talk, a description of these roots and their physical meanings will be presented. Their presence has been found in other fields. Knowledge from other fields may shed light on how these different wave modes interact under different situations. 
INI 1
15:00 to 15:30 Afternoon Tea
15:30 to 16:15 Jean-Marc Vanden-Broeck (University College London)
Asymmetric nonlinear flexural waves
Nonlinear waves travelling under an elastic sheet are considered. The fluid is assumed to be inviscid and incompressible and the flow to be irrotational. The sheet is modelled by using the theory of Plotnikov and Toland. The problem is solved by boundary integral equation methods and series truncation approaches. Periodic waves, solitary waves and generalised solitary waves are considered. Special attention is devoted to asymmetric waves. Time dependent solutions are also presented.
INI 1
16:15 to 17:00 Andrej Il’ichev (Steklov Mathematical Institute, Russian Academy of Sciences)
Wave patterns beneath an ice cover
We prove existence of the soliton-like solutions of the full system of equations which describe wave propagation in the fluid of a finite depth under an ice cover. These solutions correspond to solitary waves of various nature propagating along the water-ice interface. We consider the plane-parallel movement in a layer of the perfect fluid of the finite depth which characteristics obey the full 2D Euler system of equations. The ice cover is modeled by the elastic Kirchgoff-Love plate and it has a considerable thickness so that the plate inertia is taken into consideration when the model is formulated. The Euler equations contain the additional pressure arising from the presence of the elastic plate freely floating on the liquid surface. The mentioned families of the solitary waves are parameterized by a speed of the wave and their existence is proved for the speeds lying in some neighborhood of its critical value corresponding to the quiescent state. S olitary waves, in their turn, bifurcate from the quiescent state and lie in some neighborhood of it. By other words, existence of solitary waves of sufficiently small amplitudes on the water-ice interface is proved. The proof is conducted with the help of the projection of the required system to the central manifold and further analysis of the resulting reduced finite dimensional dynamical system on the central manifold.
INI 1
Wednesday 4th October 2017
09:00 to 09:45 Pavel Plotnikov (Lavrentyev Institute of Hydrodynamics); (Novosibirsk State University)
Conformal geometry and hydroelastic waves
INI 1
09:45 to 10:30 Mariana Haragus (Université de Franche-Comté)
Stability criteria for nonlinear waves in Hamiltonian and reversible systems
We present two general stability/instability criteria for nonlinear waves in Hamiltonian or reversible systems. Both criteria rely upon spectral properties of the linear operators found by linearizing the system at a given wave. We apply these results to some model equations arising in water-wave problems. The focus is on the question of transverse  stability/instability of periodic traveling waves.


INI 1
10:30 to 11:00 Morning Coffee
11:00 to 11:45 Timothy Williams (Natural Environment Research Council (NERC))
A sea ice model with wave-ice interactions on a moving mesh
Timothy Williams, Pierre Rampal, Einar Olason, Syvain Bouillon and Abdoulaye Samake

The neXtSIM (neXt generation Sea Ice Model) sea ice model runs the Maxwell-EB rheology solved with finite element methods on a triangular mesh. It also has thermodynamic effects and a slab ocean included beneath, as well as wave-ice interactions (ice break-up by waves, ice drift due to the wave radiation stress).

An ALE (Arbitrary Lagrangian/Eulerian) scheme has now been implemented in neXtSIM, so that the mesh is usually moving as time goes on. As part of an investigation about the best strategy for coupling the waves-in-ice module (WIM) to neXtSIM, the WIM may now be run on the neXtSIM mesh.

In this talk we give an overview of both neXtSIM and the WIM, and also some results comparing the different coupling strategies for the WIM.
INI 1
11:45 to 12:30 Yevgeny Aksenov (National Oceanography Centre, Southampton)
Impacts of ocean waves on the Polar Sea Ice and Oceans
Co-authors: Lucia Hosekova (University of Reading, UK), Danny Feltham (University of Reading, UK), Tim Williams (Nansen Environmental and Remote Sensing Center (NERSC), Norway), A.J. George Nurser (National Oceanography Centre, UK), Gurvan Madec (Institut Pierre Simon Laplace (IPSL), France), Andrew Coward (National Oceanography Centre, UK)

We examine effects of ocean surface waves on the polar sea ice and ocean using a sea ice-ocean general circulation model NEMO (stands for Nucleus for European Modelling of the Ocean) coupled with the ocean wave model WAM output from model of the European Centre for Medium-Range Weather Forecasts (ECMWF). In the model the wave-ice interactions include: ice fragmentation due to break–up by waves in the vicinity of the ice edge; wave attenuation due to multiple scattering and non-elastic losses in the ice, wave advection and evolution of ice fragmentation. We analyse the impact of the waves on sea ice and the upper ocean, focusing on the marginal ice zone (MIZ) where the wave impacts are the most. The study compares the model results with the observations, and highlights a need to farther theoretical understanding of sea ice fragmentation and summarise requirements for observational techniques. The study was carry out in the EU FP7 Project ‘Ships and waves reaching P olar Regions (SWARP)’.
INI 1
12:30 to 13:30 Lunch @ Wolfson Court
13:30 to 17:00 Free Afternoon
Thursday 5th October 2017
09:00 to 09:45 Pietro Baldi (Università degli Studi di Napoli Federico II)
Time quasi-periodic gravity water waves in finite depth
We consider the water wave equations for a 2D ocean of finite depth under the action of gravity. We present a recent existence and linear stability result for small amplitude standing wave solutions that are periodic in space and quasi-periodic in time. The result holds for values of a normalized depth parameter in a Cantor-like set of asymptotically full measure. 
The main difficulties of the problem are the presence of derivatives in the nonlinearity (the system is quasi-linear), and a small divisors problem where the frequencies of the linear part grow in a sublinear way at infinity (like the square root of integers). To overcome these problems we first reduce the linearized operators (which are obtained at each approximate quasi-periodic solution along a Nash-Moser iteration) to constant coefficients up to smoothing operators, using pseudo-differential changes of variables that are quasi-periodic in time. Then we apply a KAM reducibility scheme which requires very weak second Melnikov non-resonance conditions (losing derivatives both in time and space). Such non-resonance conditions are sufficiently weak to be satisfied for most values of the normalized depth parameter, thanks to arguments from degenerate KAM theory.
Joint work with Massimiliano Berti, Emanuele Haus and Riccardo Montalto.
INI 1
09:45 to 10:30 Mark Groves (Universität des Saarlandes); (Loughborough University)
Variational existence and stability theory for hydroelastic solitary waves
I will present an existence and stability theory for solitary waves at the interface between a thin ice sheet and an ideal fluid, which is based on minimising the total energy subject to the constraint of fixed total horizontal momentum. The ice sheet is modelled using the Cosserat theory of hyperelastic shells. Since the energy functional is quadratic in the highest derivatives, stronger results are obtained than in the corresponding theory for capillary-gravity water waves. This is joint work with Benedikt Hewer and Erik Wahlén.
INI 1
10:30 to 11:00 Morning Coffee
11:00 to 11:45 Thomas Folegot (Quiet-Oceans)
Underwater noise under ice conditions: from the ice chorus to the environmental challenge
Oceans are not silent. And this statement is even more real under ice conditions. The so-called underwater noise chorus is extremely rich and seasonally changing since it is made of multiple components: the natural sound is contributing more than in any other places since ice is a major contributor with sounds of a large diversity according to the type of ice that is present. The biological sounds are also unique in ice conditions since biodiversity in such areas are usually of exceptional nature. At last, the anthropogenic sounds are increasingly contributing to the overall noise chorus, mainly linked with the changing climate conditions that enable human maritime activities to take place. These changing conditions lead to the emerging challenge of underwater noise in ice conditions, especially in the Arctic. Underwater noise is nowadays recognized as being a serious threat for marine life and increasing international regulations are developed in many countries as per the EU Marine Strategy Framework Directive. The merging regulations appeal for new and innovative management and conservation solutions and tools.
INI 1
11:45 to 12:30 Tatiana Khabakhpasheva (University of East Anglia); (Lavrentyev Institute of Hydrodynamics)
Waves and moving loads along frozen channels
Co-authors: Shishmarev Konstantin (Altay State University, Barnaul, Russia), Korobkin Alexander (University of East Anglia, Norwich, UK)

Hydroelastic waves caused by external loads are well studied for an ice cover of infinite extent. Similar problems, but with an ice cover clamped to the vertical walls in a channel, are studied in less detail. However, the presence of the walls and clamped conditions of the ice to the walls may significantly affect distributions of deflections and stresses in the ice cover. These problems are of practical importance because laboratory experiments on loads moving along an ice cover are performed in ice tanks. The response of the ice cover caused by a moving localized external load is studied numerically and analytically for a channel with rectangular cross section. The equation of viscoelastic thin plate with a given damping coefficient is used for describing oscilations of the ice. The liquid beneath the ice is inviscid and incompressible, the flow is potential. The problem is solved with the help of the Fourier transform along the channel and the method of normal modes across the channel. The numerical results show a significant difference in the distributions of the ice deflections in the channel and in the ice cover of infinite extent for the same loading conditions. For the ice cover of infinite extent there is a single dispersion curve and two critical velocity of hydroelastic wave propagation, whereas the presence of the channel walls leads to the infinite number of the dispersion curves and critical speeds. The critical speeds depend on the channel width and decrease with increase of the distance between the walls of the channel.
INI 1
12:30 to 13:30 Lunch @ Wolfson Court
13:30 to 14:15 Stephen Ackley (University of Texas at San Antonio)
Antarctic Coastal Polynyas: Do Measurements of Winter Processes give clues to modeling Improvements and better model fidelity?
The PIPERS cruise to the Terra Nova Bay (TNB) and Ross Ice Shelf (RIS) polynyas during April-June 2017 focused on joint measurements of air-ice-ocean wave interaction in these polynyas. In Terra Nova Bay, measurements were taken during intense katabatic wind events with sustained winds over 35 meters per second and air temperatures of -15C or below. Despite a relatively short fetch, intense wave fields with wave amplitudes of over 2m and 7-9 sec periods built and large amounts of frazil ice crystals grew. The frazil ice gathered initially into short plumes that eventually were added laterally to create longer, wide streaks. The wave field within the wider streaks was dampened and enhanced the development of pancake ice. Eventually, the open water areas sealed off between the streaks, developing a uniform pancake ice cover of 100 percent concentration. The pancakes continued to grow in diameter and thickness, further attenuating the wave field and the pancake ice growt h then ceased. While the waves died off however, katabatic wind velocities were sustained and resulted in a wide area of concentrated, rafted, pancake ice that was rapidly advected downstream until the end of the katabatic event. The equilibrium thickness of the ice was typically 30 to 40 cm in the pancake ice. High resolution TerraSar-X radar satellite imagery showed the length of the ice area produced in one single event extended over 300km or ten times the length of the open water area during the polynya event. The TNB polynya is therefore an “ice factory” where frazil ice is manufactured into pancake ice floes that are then pushed out of the assembly line and advected, rafted and occasionally piled up into “dragon skin” ice, until the katabatic wind dies off at the coastal source.
INI 1
14:15 to 15:00 Alena Malyarenko (University of Otago)
Interactions between phase change and boundary layer structure
Co-authors: Pat Langhorne (University of Otago), Natalie Robinson (NIWA), Mike Williams (NIWA)

Thermodynamic ice ablation includes both melting and dissolving of the ice. Existing parametrisations are usually based on the 3-equation model, with equations that describe heat and salt flux balances together with the freezing point equation for sea water. However, these equations do not represent both melting and dissolving conditions, or the transition between these conditions. Nor do the 3 equations represent well the two dominant velocity regimes: shear-driven and buoyancy-driven mixing. Turbulent heat and salt transfer coefficients need to reflect the variety of boundary layer structures that can form under different velocity and temperature regimes.

Here the different conditions and velocity regimes are considered in the in context of multi-year observations of temperature, velocity and ablation rate from under the Ross Ice Shelf. These observations of a dissolving ice shelf in sub-zero conditions can be used to constrain transitions from buoyancy-driven mixing to sheer-driven mixing. While these observations are under an ice shelf they are expected to scale to the higher salinities found in sea ice. 
INI 1
15:00 to 15:30 Afternoon Tea
15:30 to 16:15 Jorma Kämäräinen (Finnish Transport Safety Agency)
Ship-ice-fluid interaction studies on ice resistance of ships
Ice resistance of a ship can be determined by tests made in full scale, tests made in model scale, calculations using empirical formulae, and by using numerical methods based of physical models. Model testing and the use of empirical formulae are important to ship designers, whereas the scientific community is more interested in developing real physical models. Full scale testing is important both for verification of empirical models and physical models. The purpose of this presentation is to present studies on ice resistance of ships, which are based on direct calculation methods based on modelling of physical phenomena. Ice resistance of ships in two types of ice conditions are discussed: Ship ice resistance in level ice and ship ice resistance in a brash ice channel.
INI 1
16:15 to 17:00 Discussions INI 1
19:30 to 22:00 Formal Dinner at Robinson College
Friday 6th October 2017
09:00 to 09:45 Frank Thomas Smith (University College London)
Shear flow over patches of flexible surface and related near-surface interactions
Shear flow over a three-dimensional hydroelastic surface patch or patches is considered here, modelling the interactive effects encountered well within an incident atmospheric or sea-water boundary layer. The configuration has a finite patch or an array of patches of flexible surface which are sited in an otherwise quasi-fixed solid surface. The scaled viscous-inviscid response depends on the shear, the viscosity and therefore the vorticity, as well as ice-patch parameters and three-dimensionality. Related modelling of debris, particle and ice-shard movements involves fluid/body interaction. Analysis and computations on linear and nonlinear effects often leading to flow transition are to be described.
INI 1
09:45 to 10:30 Manish Tiwari (University College London)
Impact of supercooled droplets on nanoengineered surfaces
Ice formation is commonplace in nature and manmade applications and it also influences our lives positively and sometimes catastrophically. However, a clear understanding of ice formation, role of substrate/surface on which it forms are subjects of very vigorous  current research. Icing in dynamic conditions, such as freezing of a cold drop upon hitting a surface or freezing in the presence of airflow are even less understood, despite a few novel insights developed in the last five years. This presentation will start by summarising some open and closed questions on ice formation on surfaces using nucleation theory and its extensions and report on a number of experiments to this end, which use droplet/substrate system as a model. To this end we will discuss the role of surface nanoengineering and wettability control in controlling the ice nucleation. Insights into design of icephobic surfaces with exceptional ability to delay ice formation will also be shared. The role of environmental variables such as humidity an air flow will also be discussed. Next, for the majority of the presentation, we will consider the dynamic problem of droplet and jet impacting on such surfaces reaching speeds up to ~30 m/s and Weber numbers >10,000. Droplet supercooling and its effect on droplet impact dynamics will be analysed in detail. In addition, surface morphology needs and our initial results on surface durability testing will also be presented.
INI 1
10:30 to 11:00 Morning Coffee
11:00 to 11:45 Henrik Kalisch (Universitetet i Bergen)
Fully dispersive nonlinear model equations for hydroelastic waves
INI 1
11:45 to 12:30 Ying Gou (Dalian University of Technology)
Experimental study on dead water resistance of ice floe in a two-layer fluid
Co-author: Bin Teng (University of Technology)

The dead water phenomenon is well known that when a boat is sailing on a two-layer fluid, there is an extra resistance due to the wave generating at the interface. Here, we investigate the dead water resistance of a ice floe instead of slender streamline body by three-dimensional towing experiments. The length-width ratio of ice floe is 1.5. The dimensionless ice floe draught d/h1 is varied from 0.5 to 1.0, where h1 is the upper layer depth. The Froude number Fr=U/c0 is in the range 0.3~1.3 (U towing speed, c0 the linear internal long wave speed). The experiment results show that dead water coefficient Cdw and function Cdw/(d/h1)2 attains a maximum at subcritical Froude number, Fr≈0.5~0.6, which is smaller than the previous results of slender ship. For relative small draughts, Cdw/(d/h1)2 depends on the Froude number only in the range close to critical speed (Fr>0.85), irrespective of the draught, which is same with the previous observations. But this conclusion is not applied for the case d/h1=1.0. The different variation tendency of Cdw/(d/h1)2 versus Fr is observed here. That means an extended study should be continued for deeper draught cases.
INI 1
12:30 to 13:30 Lunch @ Wolfson Court
13:30 to 14:15 Johannes E. M. Mosig (University of Otago)
Degrees of freedom in the marginal ice zone's wave--ice system
The marginal ice zones (MIZs) in both the Arctic and Southern Oceans play a key role in the Earth's climate system and the impact of sea ice on wave propagation is important to understand in order to create reliable wave forecasting models. To create efficient and accurate models of the MIZ's wave-ice system one must first identify the degrees of freedom that are relevant for such a model. In my PhD thesis and in this presentation, I will illuminate aspects of three commonly pursued paradigms: (i) floe models, where the degrees of freedom are comprised of individual ice floes; (ii) effective material models such as the one proposed by Wang and Shen (2010, dx.doi.org/10.1029/2009JC005591); and (iii) energy transport models, where the relevant degree of freedom is a single scalar field—the wave intensity—defined over the horizontal ocean domain.  

Throughout this talk I will touch upon various mathematical and computational techniques which have very general applications, yet are rarely used by the wave and sea ice community.  Specifically, I use the method framework of generalized polynomial chaos to investigate the propagation of uncertainties in various models. Moreover, I attempt to derive an analytical relationship between local scale potential flow theory, and the large-scale transport equation description of the MIZ, using a multi-scale expansion and a Wigner transform of the amplitude envelope of a propagating wave package.  

Supervisors: Vernon A. Squire, Fabien Montiel Publications: Mosig et al., Comparison of viscoelastic-type models for ocean wave attenuation in ice-covered seas, 2015, dx.doi.org/10.1002/2015JC010881 Mosig et al., Water wave scattering from a mass loading ice floe of random length using generalised polynomial chaos, dx.doi.org/10.1016/j.wavemoti.2016.09.005
INI 1
14:15 to 15:00 Usama Kadri (Cardiff University); (Massachusetts Institute of Technology)
On acoustic-gravity waves in arctic zones with elastic ice-sheets
We present an analytical solution of the boundary value problem of propagating acoustic-gravity waves generated in the ocean by earthquakes or ice-quakes in arctic zones. At the surface, we assume elastic ice-sheets of a variable thickness, and show that the propagating acoustic-gravity modes have different mode shape than originally derived by Ref. [1] for a rigid ice-sheet settings. Computationally, we couple the ice-sheet problem with the free surface model by Ref. [2] representing shrinking ice blocks in realistic sea state, where the randomly oriented ice-sheets cause inter modal transition at the edges and multidirectional reflections. We then derive a depth-integrated equation valid for spatially slowly varying thickness of ice-sheet and water depth. Surprisingly, and unlike the free-surface setting, here it is found that the higher acoustic-gravity modes exhibit a larger contribution. These modes travel at the speed of sound in water carrying information on their source, e.g. ice-sheet motion or submarine earthquake, providing various implications for ocean monitoring and detection of quakes. In addition, we found that the propagating acoustic-gravity modes can result in orbital displacements of fluid parcels sufficiently high that may contribute to deep ocean currents and circulation.
INI 1
15:00 to 15:30 Afternoon Tea
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons